# Parabola · Mathematics · JEE Main

Start Practice## Numerical

JEE Main 2024 (Online) 9th April Evening Shift

Let $$A, B$$ and $$C$$ be three points on the parabola $$y^2=6 x$$ and let the line segment $$A B$$ meet the line $$L$$ through $$C$$ parallel to the ...

JEE Main 2024 (Online) 9th April Evening Shift

Consider the circle $$C: x^2+y^2=4$$ and the parabola $$P: y^2=8 x$$. If the set of all values of $$\alpha$$, for which three chords of the circle $$C...

JEE Main 2024 (Online) 6th April Morning Shift

Let a conic $$C$$ pass through the point $$(4,-2)$$ and $$P(x, y), x \geq 3$$, be any point on $$C$$. Let the slope of the line touching the conic $$C...

JEE Main 2024 (Online) 6th April Morning Shift

Let $$L_1, L_2$$ be the lines passing through the point $$P(0,1)$$ and touching the parabola $$9 x^2+12 x+18 y-14=0$$. Let $$Q$$ and $$R$$ be the poin...

JEE Main 2024 (Online) 5th April Evening Shift

Let a line perpendicular to the line $$2 x-y=10$$ touch the parabola $$y^2=4(x-9)$$ at the point P. The distance of the point P from the centre of the...

JEE Main 2024 (Online) 5th April Morning Shift

Suppose $$\mathrm{AB}$$ is a focal chord of the parabola $$y^2=12 x$$ of length $$l$$ and slope $$\mathrm{m}...

JEE Main 2024 (Online) 4th April Morning Shift

Let the length of the focal chord PQ of the parabola $$y^2=12 x$$ be 15 units. If the distance of $$\mathrm{PQ}$$ from the origin is $$\mathrm{p}$$, t...

JEE Main 2024 (Online) 1st February Morning Shift

Let the line $\mathrm{L}: \sqrt{2} x+y=\alpha$ pass through the point of the intersection $\mathrm{P}$ (in the first quadrant) of the circle $x^2+y^2=...

JEE Main 2024 (Online) 29th January Evening Shift

Let $$P(\alpha, \beta)$$ be a point on the parabola $$y^2=4 x$$. If $$P$$ also lies on the chord of the parabola $$x^2=8 y$$ whose mid point is $$\lef...

JEE Main 2023 (Online) 11th April Evening Shift

Let the tangent to the parabola $$\mathrm{y}^{2}=12 \mathrm{x}$$ at the point $$(3, \alpha)$$ be perpendicular to the line $$2 x+2 y=3$$. Then the squ...

JEE Main 2023 (Online) 10th April Morning Shift

Let a common tangent to the curves $${y^2} = 4x$$ and $${(x - 4)^2} + {y^2} = 16$$ touch the curves at the points P and Q. Then $${(PQ)^2}$$ is equal ...

JEE Main 2023 (Online) 8th April Evening Shift

The ordinates of the points P and $$\mathrm{Q}$$ on the parabola with focus $$(3,0)$$ and directrix $$x=-3$$ are in the ratio $$3: 1$$. If $$\mathrm{R...

JEE Main 2023 (Online) 6th April Morning Shift

Let the tangent to the curve $$x^{2}+2 x-4 y+9=0$$ at the point $$\mathrm{P}(1,3)$$ on it meet the $$y$$-axis at $$\mathrm{A}$$. Let the line passing ...

JEE Main 2023 (Online) 1st February Evening Shift

If the $$x$$-intercept of a focal chord of the parabola $$y^{2}=8x+4y+4$$ is 3, then the length of this chord is equal to ____________.

JEE Main 2023 (Online) 31st January Evening Shift

Let $\mathrm{S}$ be the set of all $\mathrm{a} \in \mathrm{N}$ such that the area of the triangle formed by the tangent at the point $\mathrm{P}(\math...

JEE Main 2023 (Online) 29th January Evening Shift

A triangle is formed by the tangents at the point (2, 2) on the curves $$y^2=2x$$ and $$x^2+y^2=4x$$, and the line $$x+y+2=0$$. If $$r$$ is the radius...

JEE Main 2022 (Online) 28th July Evening Shift

Two tangent lines $$l_{1}$$ and $$l_{2}$$ are drawn from the point $$(2,0)$$ to the parabola $$2 \mathrm{y}^{2}=-x$$. If the lines $$l_{1}$$ and $$l_{...

JEE Main 2022 (Online) 25th July Morning Shift

The sum of diameters of the circles that touch (i) the parabola $$75 x^{2}=64(5 y-3)$$ at the point $$\left(\frac{8}{5}, \frac{6}{5}\right)$$ and (ii)...

JEE Main 2022 (Online) 30th June Morning Shift

Let PQ be a focal chord of length 6.25 units of the parabola y2 = 4x. If O is the vertex of the parabola, then 10 times the area (in sq. units) of $$\...

JEE Main 2022 (Online) 27th June Morning Shift

A circle of radius 2 unit passes through the vertex and the focus of the parabola y2 = 2x and touches the parabola $$y = {\left( {x - {1 \over 4}} \ri...

JEE Main 2022 (Online) 26th June Morning Shift

Let the common tangents to the curves $$4({x^2} + {y^2}) = 9$$ and $${y^2} = 4x$$ intersect at the point Q. Let an ellipse, centered at the origin O, ...

JEE Main 2022 (Online) 24th June Evening Shift

Let P1 be a parabola with vertex (3, 2) and focus (4, 4) and P2 be its mirror image with respect to the line x + 2y = 6. Then the directrix of P2 is x...

JEE Main 2021 (Online) 31st August Evening Shift

A tangent line L is drawn at the point (2, $$-$$4) on the parabola y2 = 8x. If the line L is also tangent to the circle x2 + y2 = a, then 'a' is equa...

JEE Main 2021 (Online) 20th July Evening Shift

If the point on the curve y2 = 6x, nearest to the point $$\left( {3,{3 \over 2}} \right)$$ is ($$\alpha$$, $$\beta$$), then 2($$\alpha$$ + $$\beta$$) ...

JEE Main 2021 (Online) 20th July Morning Shift

Let y = mx + c, m > 0 be the focal chord of y2 = $$-$$ 64x, which is tangent to (x + 10)2 + y2 = 4. Then, the value of 4$$\sqrt 2 $$ (m + c) is equ...

JEE Main 2021 (Online) 25th February Evening Shift

A line is a common tangent to the circle (x $$-$$ 3)2 + y2 = 9 and the parabola y2 = 4x. If the two points of contact (a, b) and (c, d) are distinct a...

JEE Main 2020 (Online) 3rd September Evening Slot

If the tangent to the curve, y = ex
at a point
(c, ec) and the normal to the parabola, y2 = 4x
at the point (1, 2) intersect at the same point on
the...

JEE Main 2020 (Online) 8th January Evening Slot

Let a line y = mx (m > 0) intersect the parabola,
y2 = x at a point P, other than the origin. Let
the tangent to it at P meet the x-axis at the poi...

## MCQ (Single Correct Answer)

JEE Main 2024 (Online) 6th April Morning Shift

Let $$C$$ be the circle of minimum area touching the parabola $$y=6-x^2$$ and the lines $$y=\sqrt{3}|x|$$. Then, which one of the following points lie...

JEE Main 2024 (Online) 4th April Evening Shift

Let $$P Q$$ be a chord of the parabola $$y^2=12 x$$ and the midpoint of $$P Q$$ be at $$(4,1)$$. Then, which of the following point lies on the line p...

JEE Main 2024 (Online) 27th January Morning Shift

If the shortest distance of the parabola $y^2=4 x$ from the centre of the circle $x^2+y^2-4 x-16 y+64=0$ is $\mathrm{d}$, then $\mathrm{d}^2$ is equal...

JEE Main 2023 (Online) 13th April Morning Shift

Let $$\mathrm{PQ}$$ be a focal chord of the parabola $$y^{2}=36 x$$ of length 100 , making an acute angle with the positive $$x$$-axis. Let the ordina...

JEE Main 2023 (Online) 8th April Evening Shift

Let $$\mathrm{A}(0,1), \mathrm{B}(1,1)$$ and $$\mathrm{C}(1,0)$$ be the mid-points of the sides of a triangle with incentre at the point $$\mathrm{D}$...

JEE Main 2023 (Online) 8th April Morning Shift

Let $$R$$ be the focus of the parabola $$y^{2}=20 x$$ and the line $$y=m x+c$$ intersect the parabola at two points $$P$$ and $$Q$$.
Let the point $$...

JEE Main 2023 (Online) 31st January Morning Shift

Let $$\mathrm{y}=f(x)$$ represent a parabola with focus $$\left(-\frac{1}{2}, 0\right)$$ and directrix $$y=-\frac{1}{2}$$. Then
$$S=\left\{x \in \mat...

JEE Main 2023 (Online) 30th January Evening Shift

Let $A$ be a point on the $x$-axis. Common tangents are drawn from $A$ to the curves $x^2+y^2=8$ and $y^2=16 x$. If one of these tangents touches the ...

JEE Main 2023 (Online) 30th January Evening Shift

The parabolas : $a x^2+2 b x+c y=0$ and $d x^2+2 e x+f y=0$ intersect on the line $y=1$. If $a, b, c, d, e, f$ are positive real numbers and $a, b, c$...

JEE Main 2023 (Online) 30th January Morning Shift

If $$\mathrm{P}(\mathrm{h}, \mathrm{k})$$ be a point on the parabola $$x=4 y^{2}$$, which is nearest to the point $$\mathrm{Q}(0,33)$$, then the dista...

JEE Main 2023 (Online) 29th January Evening Shift

If the tangent at a point P on the parabola $$y^2=3x$$ is parallel to the line $$x+2y=1$$ and the tangents at the points Q and R on the ellipse $$\fra...

JEE Main 2023 (Online) 25th January Evening Shift

The equations of two sides of a variable triangle are $$x=0$$ and $$y=3$$, and its third side is a tangent to the parabola $$y^2=6x$$. The locus of it...

JEE Main 2023 (Online) 25th January Morning Shift

The distance of the point $$(6,-2\sqrt2)$$ from the common tangent $$\mathrm{y=mx+c,m > 0}$$, of the curves $$x=2y^2$$ and $$x=1+y^2$$ is :

JEE Main 2023 (Online) 24th January Evening Shift

The equations of the sides AB and AC of a triangle ABC are $$(\lambda+1)x+\lambda y=4$$ and $$\lambda x+(1-\lambda)y+\lambda=0$$ respectively. Its ver...

JEE Main 2023 (Online) 24th January Morning Shift

Let a tangent to the curve $$\mathrm{y^2=24x}$$ meet the curve $$xy = 2$$ at the points A and B. Then the mid points of such line segments AB lie on a...

JEE Main 2022 (Online) 29th July Morning Shift

Let the focal chord of the parabola $$\mathrm{P}: y^{2}=4 x$$ along the line $$\mathrm{L}: y=\mathrm{m} x+\mathrm{c}, \mathrm{m}>0$$ meet the parabola...

JEE Main 2022 (Online) 28th July Morning Shift

If the tangents drawn at the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ on the parabola $$y^{2}=2 x-3$$ intersect at the point $$R(0,1)$$, then the orth...

JEE Main 2022 (Online) 27th July Evening Shift

If the length of the latus rectum of a parabola, whose focus is $$(a, a)$$ and the tangent at its vertex is $$x+y=a$$, is 16, then $$|a|$$ is equal to...

JEE Main 2022 (Online) 27th July Morning Shift

Let $$P(a, b)$$ be a point on the parabola $$y^{2}=8 x$$ such that the tangent at $$P$$ passes through the centre of the circle $$x^{2}+y^{2}-10 x-14 ...

JEE Main 2022 (Online) 26th July Evening Shift

Let $$\mathrm{P}$$ and $$\mathrm{Q}$$ be any points on the curves $$(x-1)^{2}+(y+1)^{2}=1$$ and $$y=x^{2}$$, respectively. The distance between $$P$$ ...

JEE Main 2022 (Online) 26th July Evening Shift

The equation of a common tangent to the parabolas $$y=x^{2}$$ and $$y=-(x-2)^{2}$$ is

JEE Main 2022 (Online) 25th July Evening Shift

The tangents at the points $$A(1,3)$$ and $$B(1,-1)$$ on the parabola $$y^{2}-2 x-2 y=1$$ meet at the point $$P$$. Then the area (in unit $${ }^{2}$$ ...

JEE Main 2022 (Online) 29th June Evening Shift

Let P : y2 = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of $${\pi \over 4}$$ with the line y = 3x + 5 to...

JEE Main 2022 (Online) 29th June Morning Shift

Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of $${\pi \over 2}$$ at the point (3, 0). Let the line segment PQ be a...

JEE Main 2022 (Online) 28th June Evening Shift

If vertex of a parabola is (2, $$-$$1) and the equation of its directrix is 4x $$-$$ 3y = 21, then the length of its latus rectum is :

JEE Main 2022 (Online) 27th June Evening Shift

If the equation of the parabola, whose vertex is at (5, 4) and the directrix is $$3x + y - 29 = 0$$, is $${x^2} + a{y^2} + bxy + cx + dy + k = 0$$, th...

JEE Main 2022 (Online) 26th June Morning Shift

Let the normal at the point on the parabola y2 = 6x pass through the point (5, $$-$$8). If the tangent at P to the parabola intersects its directrix a...

JEE Main 2022 (Online) 25th June Evening Shift

If the line $$y = 4 + kx,\,k > 0$$, is the tangent to the parabola $$y = x - {x^2}$$ at the point P and V is the vertex of the parabola, then the slop...

JEE Main 2022 (Online) 25th June Morning Shift

If $$y = {m_1}x + {c_1}$$ and $$y = {m_2}x + {c_2}$$, $${m_1} \ne {m_2}$$ are two common tangents of circle $${x^2} + {y^2} = 2$$ and parabola y2 = x,...

JEE Main 2022 (Online) 25th June Morning Shift

Let $$x = 2t$$, $$y = {{{t^2}} \over 3}$$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $$SA \bot BA$$, where A...

JEE Main 2022 (Online) 24th June Evening Shift

A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q...

JEE Main 2022 (Online) 24th June Morning Shift

Let x2 + y2 + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x2 at (2, 4). Then A + C is equal to ___________....

JEE Main 2021 (Online) 1st September Evening Shift

Consider the parabola with vertex $$\left( {{1 \over 2},{3 \over 4}} \right)$$ and the directrix $$y = {1 \over 2}$$. Let P be the point where the par...

JEE Main 2021 (Online) 31st August Morning Shift

The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (> R) respectively from the o...

JEE Main 2021 (Online) 27th August Evening Shift

If two tangents drawn from a point P to the parabola y2 = 16(x $$-$$ 3) are at right angles, then the locus of point P is :

JEE Main 2021 (Online) 27th August Morning Shift

A tangent and a normal are drawn at the point P(2, $$-$$4) on the parabola y2 = 8x, which meet the directrix of the parabola at the points A and B res...

JEE Main 2021 (Online) 25th July Morning Shift

Let a parabola b be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 units from the origin, respectively. If tangents a...

JEE Main 2021 (Online) 20th July Evening Shift

Let P be a variable point on the parabola $$y = 4{x^2} + 1$$. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn ...

JEE Main 2021 (Online) 20th July Morning Shift

Let the tangent to the parabola S : y2 = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the ar...

JEE Main 2021 (Online) 17th March Evening Shift

Let L be a tangent line to the parabola y2 = 4x $$-$$ 20 at (6, 2). If L is also a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$...

JEE Main 2021 (Online) 16th March Evening Shift

Let C be the locus of the mirror image of a point on the parabola y2 = 4x with respect to the line y = x. Then the equation of tangent to C at P(2, 1)...

JEE Main 2021 (Online) 16th March Morning Shift

If the three normals drawn to the parabola, y2 = 2x pass through the point (a, 0) a $$\ne$$ 0, then 'a' must be greater than :

JEE Main 2021 (Online) 25th February Evening Shift

The shortest distance between the line x $$-$$ y = 1 and the curve x2 = 2y is :

JEE Main 2021 (Online) 25th February Morning Shift

A tangent is drawn to the parabola y2 = 6x which is perpendicular to the line 2x + y = 1. Which of the following points does NOT lie on it?

JEE Main 2021 (Online) 24th February Evening Shift

If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x $$-$$ 1, then the co-ordinates of P are :

JEE Main 2021 (Online) 24th February Morning Shift

The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a
moving point of the parabola, is another parabola whose...

JEE Main 2020 (Online) 6th September Evening Slot

The centre of the circle passing through the
point (0, 1) and touching the parabola y = x2 at the point (2, 4) is :

JEE Main 2020 (Online) 6th September Morning Slot

Let L1
be a tangent to the parabola y2 = 4(x + 1) and L2
be a tangent to the parabola
y2 = 8(x + 2) such that L1
and L2
intersect at right angles....

JEE Main 2020 (Online) 5th September Morning Slot

If the common tangent to the parabolas, y2 = 4x and x2 = 4y also touches the circle, x2 + y2 = c2, then c is equal to :...

JEE Main 2020 (Online) 3rd September Evening Slot

Let the latus ractum of the parabola y2
= 4x be
the common chord to the circles C1
and C2
each of them having radius 2$$\sqrt 5 $$. Then, the
distan...

JEE Main 2020 (Online) 3rd September Morning Slot

Let P be a point on the parabola, y2
= 12x and
N be the foot of the perpendicular drawn from
P on the axis of the parabola. A line is now
drawn throu...

JEE Main 2020 (Online) 2nd September Evening Slot

The area (in sq. units) of an equilateral triangle
inscribed in the parabola y2 = 8x, with one of
its vertices on the vertex of this parabola, is :...

JEE Main 2020 (Online) 9th January Evening Slot

If one end of a focal chord AB of the parabola
y2 = 8x is at $$A\left( {{1 \over 2}, - 2} \right)$$, then the equation of
the tangent to it at B is :...

JEE Main 2020 (Online) 8th January Morning Slot

The locus of a point which divides the line
segment joining the point (0, –1) and a point on
the parabola, x2 = 4y, internally in the ratio
1 : 2, is ...

JEE Main 2020 (Online) 7th January Morning Slot

If y = mx + 4 is a tangent to both the parabolas, y2 = 4x and x2 = 2by, then b is equal to :

JEE Main 2019 (Online) 12th April Evening Slot

The equation of common tangent to the curves y2
= 16x and xy = –4, is :

JEE Main 2019 (Online) 12th April Evening Slot

The tangents to the curve y = (x – 2)2 – 1 at its points of intersection with the line x – y = 3, intersect at the point :

JEE Main 2019 (Online) 12th April Morning Slot

Let P be the point of intersection of the common tangents to the parabola y2
= 12x and the hyperbola
8x2
– y2
= 8. If S and S' denote the foci of th...

JEE Main 2019 (Online) 10th April Evening Slot

If the line ax + y = c, touches both the curves x2
+ y2
= 1 and y2
= 4$$\sqrt 2 $$x , then |c| is equal to :

JEE Main 2019 (Online) 9th April Evening Slot

The area (in sq. units) of the smaller of the two
circles that touch the parabola, y2 = 4x at the point
(1, 2) and the x-axis is :-

JEE Main 2019 (Online) 9th April Morning Slot

If one end of a focal chord of the parabola,
y2 = 16x is at (1, 4), then the length of this focal
chord is :

JEE Main 2019 (Online) 8th April Evening Slot

The tangent to the parabola y2
= 4x at the point
where it intersects the circle x2
+ y2
= 5 in the
first quadrant, passes through the point :
...

JEE Main 2019 (Online) 8th April Morning Slot

The shortest distance between the line y = x and
the curve y2 = x – 2 is :

JEE Main 2019 (Online) 12th January Evening Slot

The equation of a tangent to the parabola, x2
= 8y, which makes an angle $$\theta $$ with the positive directions of x-axis, is :

JEE Main 2019 (Online) 12th January Morning Slot

The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, y = 12 – x2 such that the re...

JEE Main 2019 (Online) 12th January Morning Slot

Let P(4, –4) and Q(9, 6) be two points on the parabola, y2 = 4x and let x be any point on the arc POQ of this parabola, where O is the vertex of this ...

JEE Main 2019 (Online) 11th January Evening Slot

If the area of the triangle whose one vertex is at the vertex of the parabola, y2 + 4(x – a2) = 0 and the othertwo vertices are the points of intersec...

JEE Main 2019 (Online) 10th January Evening Slot

The length of the chord of the parabola x2 $$=$$ 4y having equation x – $$\sqrt 2 y + 4\sqrt 2 = 0$$ is -

JEE Main 2019 (Online) 10th January Morning Slot

If the parabolas y2 = 4b(x – c) and y2 = 8ax have a common normal, then which on of the following is a valid choice for the ordered triad (a, b, c)?...

JEE Main 2019 (Online) 9th January Evening Slot

Let A(4, $$-$$ 4) and B(9, 6) be points on the parabola, y2 = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the...

JEE Main 2019 (Online) 9th January Morning Slot

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the
origin, on the positive x-axis then which...

JEE Main 2019 (Online) 9th January Morning Slot

Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x is :

JEE Main 2019 (Online) 9th January Morning Slot

If $$\theta $$ denotes the acute angle between the curves, y = 10 – x2 and y = 2 + x2 at a point of their intersection, the |tan $$\theta $$| is equa...

JEE Main 2018 (Online) 16th April Morning Slot

Let P be a point on the parabola, x2 = 4y. If the distance of P from the center of the circle, x2 + y2 + 6x + 8 = 0 is minimum, then the equation of ...

JEE Main 2018 (Offline)

Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the
parabola at A and B, respectively. If C is the cen...

JEE Main 2018 (Online) 15th April Evening Slot

Tangents drawn from the point ($$-$$8, 0) to the parabola y2 = 8x touch the parabola at $$P$$ and $$Q.$$ If F is the focus of the parabola, then the a...

JEE Main 2018 (Online) 15th April Morning Slot

Two parabolas with a common vertex and with axes along x-axis and $$y$$-axis, respectively intersect each other in the first quadrant. If the length o...

JEE Main 2017 (Online) 9th April Morning Slot

If y = mx + c is the normal at a point on the parabola y2 = 8x whose focal distance is 8 units, then $$\left| c \right|$$ is equal to :

JEE Main 2017 (Online) 8th April Morning Slot

If the common tangents to the parabola, x2 = 4y and the circle, x2 + y2 = 4 intersect at the point P, then the distance of P from the origin, is : ...

JEE Main 2016 (Online) 10th April Morning Slot

P and Q are two distinct points on the parabola, y2 = 4x, with parameters t and t1 respectively. If the normal at P passes through Q, then the minimum...

JEE Main 2016 (Offline)

Let $$P$$ be the point on the parabola, $${{y^2} = 8x}$$ which is at a minimum distance from the centre $$C$$ of the circle, $${x^2} + {\left( {y + 6}...

JEE Main 2015 (Offline)

Let $$O$$ be the vertex and $$Q$$ be any point on the parabola, $${{x^2} = 8y}$$. If the point $$P$$ divides the line segment $$OQ$$ internally in the...

JEE Main 2014 (Offline)

The slope of the line touching both the parabolas $${y^2} = 4x$$ and $${x^2} = - 32y$$ is

JEE Main 2013 (Offline)

Given : A circle, $$2{x^2} + 2{y^2} = 5$$ and a parabola, $${y^2} = 4\sqrt 5 x$$.
Statement-1 : An equation of a common tangent to these curves is $$...

AIEEE 2010

If two tangents drawn from a point $$P$$ to the parabola $${y^2} = 4x$$ are at right angles, then the locus of $$P$$ is

AIEEE 2008

A parabola has the origin as its focus and the line $$x=2$$ as the directrix. Then the vertex of the parabola is at :

AIEEE 2007

The equation of a tangent to the parabola $${y^2} = 8x$$ is $$y=x+2$$. The point on this line from which the other tangent to the parabola is perpendi...

AIEEE 2006

The locus of the vertices of the family of parabolas
$$y = {{{a^3}{x^2}} \over 3} + {{{a^2}x} \over 2} - 2a$$ is :

AIEEE 2005

Let $$P$$ be the point $$(1, 0)$$ and $$Q$$ a point on the parabola $${y^2} = 8x$$. The locus of mid point of $$PQ$$ is :

AIEEE 2004

If $$a \ne 0$$ and the line $$2bx+3cy+4d=0$$ passes through the points of intersection of the parabolas $${y^2} = 4ax$$ and $${x^2} = 4ay$$, then :

AIEEE 2003

The normal at the point$$\left( {bt_1^2,2b{t_1}} \right)$$ on a parabola meets the parabola again in the point $$\left( {bt_2^2,2b{t_2}} \right)$$, th...

AIEEE 2002

Two common tangents to the circle $${x^2} + {y^2} = 2{a^2}$$ and parabola $${y^2} = 8ax$$ are :